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Representations of Hom-Jacobi-Jordan algebras are studied. In particular,adjoint representations and trivial representations are studied in detail.Derivations and central extensions of Hom-Jacobi-Jordan algebras are alsodiscussed as an application. Morover, we introduce the cohomology theory onHom-Jacobi-Jordan algebras as well as the one of relative Rota-Baxter operatorson Hom-Jacobi-Jordan algebras. Finally, we use the cohomological approach tostudy deformations of Hom-Jacobi-Jordan algebras and those of relativeRota-Baxter operators.

Deformations of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras